In how many seconds from the beginning of the countdown, the body will stop if the equation

In how many seconds from the beginning of the countdown, the body will stop if the equation of motion of the body is S = 40t-0.1t ^ 2.

Initial data: the equation of body motion S (t) = 40t – 0.1t ^ 2; V (final velocity of the body) = 0 m / s.

1) The law by which the speed of a body changes (it is necessary to take the first-order derivative from the equation of motion): V = S ‘= (40t – 0.1t ^ 2)’ = 40 * 1 – 0.1 * 2 * t = 40 – 0.2t.

2) The time when the body completely stops:

0 = 40 – 0.2t.

40 = 0.2t.

t = 40 / 0.2 = 200 s or 3 min 20 s.

Answer: The body will stop 3 minutes 20 seconds after the start of the countdown.